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Let $n > 2$ and let $A$ be a real and singular (i.e., non-invertible) $n\times n$ matrix. Is it true that $adj(adj(A)) = 0$ ?

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  • $\begingroup$ A stronger result: see here or here. $\endgroup$ – user37238 Jan 29 '16 at 11:28
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Hint : What is the adjugate matrix is the rank of A is strictly less than $n-1$? And what is the rank of $\text{adj}(A)$ when $\text{rk}(A)=n-1$?

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